Why do some bones in this rig only update their position correctly when I press G?
When something doesn't update properly like this it is often caused by a Dependency Cycle. Opening the System Console with Window&gt; Toggle System Console (this option is only available on Windows) you see the message:

Dependency cycle detected:
rig depends on MCH_armSpline.L through Spline IK.
MCH_armSpline.L depends on rig through Hook Modifier.

A dependency cycle is where &quot;Object A&quot; depends on &quot;Object B&quot; for its position, but &quot;Object B&quot; depends on &quot;Object A&quot; for its position. They each depend on each other and as Blender can't determine which object needs to be updated first, it stops updating them.
The Depsgraph - the part of blender which handles these object updates - is currently undergoing a major update and so this type of behaviour might not be an issue in future.
The current 'solution' is to avoid these types of rig hierarchies in the first place. Unfortunately, this is a fairly complex rig so I'm unable to see how you might solve this and still retain the rig's functionality, so you may want to contact the author of the tutorial with this information to see if they can offer a fix.